(the pdfs may differ from the final published version)
- (submitted) Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces (with C. Fefferman, D. McCormick, & J. Robinson)
- (submitted) Lower bounds on blowing-up solutions of the 3D Navier–Stokes equations in $ \dot{H}^{3/2} $, $ \dot{H}^{3/2} $ and $\dot{B}^{5/2}_{2,1} $, ( with D. McCormick, E. Olson, J.C. Robinson, A. Vidal-Lopez
& Y. Zhou)
- Local existence for the non-resistive MHD equations in Besov spaces. Advances in Mathematics (2016) Vol 286, 1-31 (with J-Y Chemin, D. McCormick & J.C.
Robinson)
- Construction of analytic almost sharp fronts. Archive for Rational Mechanics and Applications (2015), Vol 218, 123-162 (with Charles Fefferman).
- Higher order commutator estimates and local existence for the non-resistive MHD equations and related models. Journal of Functional Analysis (2014) Vol 267, 1035-
1056. (with C. Fefferman, D.S. McCormick, and
J.C. Robinson)
- Existence and uniqueness for a coupled elliptic parabolic model with applications
to magnetic relaxation. Archives for Rational Mechanics and Analysis (2014), Vol 214, 503-523 (with James C. Robinson & David S. McCormick).
- Generalised Gagliardo Nirenberg inequalities using weak Lebesgue spaces and BMO, accepted in the Milan Journal of Mathematics (2013), Vol 81, no. 2, 265-289, (with James C. Robinson & D. S. McCormick).
- Almost Sharp Fronts for SQG: the limit equations, Comm. Math. Phys. 313, (2012),
131 153, (with Charles Fefferman)
- The spine of an SQG almost sharp front, Nonlinearity 25 (2012), 329 342, (with Charles
Fefferman & Kevin Luli)
- Analytic Sharp Fronts for SQG, Comm. Math. Phys. 303 (2011), no. 1, 261 288 (with Charles Fefferman)
- Almost Sharp Fronts for SQG: the limit equations, Comm. Math. Phys. 313, (2012),
131 153, (with Charles Fefferman)
- The spine of an SQG almost sharp front, Nonlinearity 25 (2012), 329 342, (with Charles
Fefferman & Kevin Luli)
- Analytic Sharp Fronts for SQG, Comm. Math. Phys. 303 (2011), no. 1, 261 288 (with Charles Fefferman)
- On a One-Dimensional Nonlocal Flux with Fractional Dissipation, SIAM J. Math. Anal. 43 (2011), 507 526 (with Dong Li)
- Exploding solutions for a nonlocal quadratic evolution problem, Revista Matematica Iberoamericana 26 (2010), no. 1, 295 332( with Dong Li and Xiaoyi Zhang) pdf
- Wellposedness and regularity of solutions of an aggregation equation, Revista Matematica Iberoamericana 26 (2010), no. 1, 261 294( with Dong Li) pdf
- Refined blowup criteria and nonsymmetric blowup of an aggregation equation, Advances in Mathematics 220, 6, (2009), 1717 1738.( with Dong Li) pdf
- Finite-time singularities of an aggregation equation in R^n with fractional
dissipation, Comm. Math. Phys. 287 (2009), no. 2, 687 703 ( with Dong Li) pdf
- Contour dynamics for the surface quasi-geostrophic equation, in Partial Differential Equations and Fluid Mechanics. London Mathematical Society Lecture Note Series (No. 364).
- Blow up for the generalized surface quasi-geostrophic
equation with supercritical dissipation, Comm. Math. Phys. 286 (2009), no. 1, 111 124( with Dong Li) pdf
-
Blow up of solutions for a 1D transport equation with nonlocal velocity
and supercritical dissipation, Advances in Mathematics, 217, no. 6, 2563 2568 (2008.
(with Dong Li) pdf
- On the evolution of sharp fronts for the
quasi-geostrophic equation. Comm. Pure Appl. Math. 58, no. 6, 821 866
(2005). pdf
- Evidence of singularities for a family of contour
dynamics equations. (with D. Cordoba, M. A. Fontelos and A. M. Mancho) PNAS Vol 102, n 17, 5949 5952, April 26 (2005).
PNAS link
pdf
- The vortex patch problem for the Quasi-Geostrophic
equation.
PNAS Vol 101, n 9, 2484 2486, March 2 (2004).
(PNAS link) pdf
- Almost sharp fronts for the surface Quasi-Geostrophic
equation.
(with D. Cordoba and C. Fefferman)
PNAS Vol 101, n 9, 2487 2491, March 2 (2004).
PNAS link pdf